Product form solution for G-networks with dependent service

We consider a G-network with Poisson flow of positive customers. Each positive customer entering the network is characterized by a set of stochastic parameters: customer route, the length of customer route, customer volume and his service length at each route stage as weH. The following node types are considered: (0) an exponential node with Cn servers, infinite buffer and FIFO discipline; (1) an infinite-server node; (2) a single-server node with infinite buffer and LIFO PR discipline; (3) a single-server node with infinite buffer and PS discipline. Negative customers arriving at each node also form a Poisson flow. A negative customer entering a node with k customers in service, with probability, 1/k chooses one of served positive customer as a "target". Then, if the node is of a type 0 the negative customer immediately "kills" (displaces from the network) the target customer, and if the node is of types 1-3 the negative customer with given probability depending on parameters of the target customer route kills this customer and with complementary probability he quits the network with no service. A product form for the stationary probabilities of underlying Markov process is obtained.

Авторы
Bocharov P. 1 , D'Apice C.2 , Gavrilov E. 1 , Pechinkin A. 3
Номер выпуска
2
Язык
Английский
Страницы
105-119
Статус
Опубликовано
Том
38
Год
2004
Организации
  • 1 Department of Probability Theory, Peoples' Friendship Univ. of Russia, Moscow, Russian Federation
  • 2 Dept. of Information Engineering, University of Salerno, Italy
  • 3 Institute of Informatics Problems, Russian Academy of Sciences, Moscow, Russian Federation
Ключевые слова
Image compression; Mathematical models; Neural networks; Queueing networks; Random processes; Telecommunication networks; G networks; Poisson flow; Stochastic parameters; Operations research
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/3656/
Поделиться

Другие записи